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For the purposes of this problem, use the following data: mass of Comet 67P is 1...
On November 12, 2014, the Philae lander separated from the European Space Agency's Rosetta spacecraft, and...
On November 12, 2014, the Philae lander separated from the European Space Agency's Rosetta spacecraft, and made a lancing (after bouncing twice) on a comet known as 67P/Chunyumov -Gerasimenko. In this problem, we will explore the Gravitational environment that Rosetta (orbiting the comet) and Philae (on the comet's surface) experienced. On September 30, 2016, Rosetta crashed (as planned) on the comet. We will use a very simple model of the comet, modeling it as a perfect sphere. This is not...
A comet moves about the Sun in an elliptical orbit, with its closest approach to the...
A comet moves about the Sun in an elliptical orbit, with its closest approach to the Sun being about 0.620 AU and its greatest distance from the sun being 35.5 AU (1 AU = the Earth-Sun distance). If the comet's speed at closest approach is 54.0 km/s, what is its speed when it is farthest from the Sun? (The gravitational force exerted by the Sun on the comet is parallel to the moment arm, so exerts no torque. Therefore, angular...
Problem 2: Haley's Comet (A Real Life Example): Important: for this problem, complete all numerical work...
Problem 2: Haley's Comet (A Real Life Example): Important: for this problem, complete all numerical work to a precision of at least six significant digits. Specifically: use the following precise values for astronomical constants: • Mass of the Sun = 1.98855 x 1030 kg • 1 AU = 149,597,870,700 meters . G=6.67384 x 10-11 N·m²/kg? Neptune Uranus Saturn Jupiter 05 2000 2005 2000----1995 2010 19921989 1988 1987 2024 1986 2061 2040 2060 2045 2050 2055 2056 2057 2058 2059 In...
8. A comet with unknown mass mc is in an elliptical orbit around the sun: R....
8. A comet with unknown mass mc is in an elliptical orbit around the sun: R. Rp mc mc MS ū When the comet is at its parahelion R, it has a speed of up = 80km/s and at its aphelion R, it has a speed of va = 10km/s. For this problem suppose we do not know the mass of the sun M, or the value of Newton's constant G, but we can approximate the orbit of the earth...
Problem 3: The Rosetta spacecraft landed a probe on the comet Churyumov-Gerasimenko. It has a mass...
Problem 3: The Rosetta spacecraft landed a probe on the comet Churyumov-Gerasimenko. It has a mass of appeoximately 1 x 10 kg and has an average density of approximately 400 kg/m. It is far from spherical, but for this problem go ahead and assume it is spherical. Estimate the radius, the acceleration due to gravity at the surface and the escape velocity from its surface. (10 points) Problem 4: A GPS satellite has a mass of 1940 kg and is...
Astronomers have discovered a new comet that’s moving at 53 km/s as it crosses Earth’s orbit....
Astronomers have discovered a new comet that’s moving at 53 km/s as it crosses Earth’s orbit. The comet then passes the Sun and heads off into space. Will it ever return? The Sun’s mass is 2 × 1030 kg and the radius of Earth’s orbit is 1.5 × 1011 m.
QUESTION 1: The International Space Station has a mass of 4.19 ✕ 105 kg and orbits...
QUESTION 1: The International Space Station has a mass of 4.19 ✕ 105 kg and orbits at a radius of 6.79 ✕ 106 m from the center of Earth. Find the gravitational force exerted by Earth on the space station, the space station's gravitational potential energy, and the weight of a 92.3 kgastronaut living inside the station. HINT (a) the gravitational force (in N) exerted by Earth on the space station (Enter the magnitude.) N (b) the space station's gravitational...
6. When Halley's comet is closest to the Sun, it is at a distance of 8.823x1010...
6. When Halley's comet is closest to the Sun, it is at a distance of 8.823x1010 m from the Sun and at a speed of 5.46x 104 m/s. Given the comet's mass is about 2.2x1014 kg and the Sun's mass is 2.00x1020 kg: (a) Find the total mechanical energy of Halley's comet (8 points) (b) Assume all the time Hallye's comet is subject to the Sun's gravitational pull only. As the comet moves further away from the Sun, what will...
An exoplanet is in an elliptical orbit around a distant star. At its closest approach, the...
An exoplanet is in an elliptical orbit around a distant star. At its closest approach, the exoplanet is 0.530 AU from the star and has a speed of 54.0 km/s. When the exoplanet is at its farthest distance from the star of 33.0 AU, what is its speed (in km/s)? (1 AU is the average distance from the Earth to the Sun and is equal to 1.496 ✕ 1011 m. You may assume that other planets and smaller objects in...
A comet orbits the Sun and loses mass at a constant rate of 30,000kg/s. The only...
A comet orbits the Sun and loses mass at a constant rate of
30,000kg/s. The only force acting on the comet is the gravitational
force.
a) From the definition of torque in terms of angular momentum,
torque=dL/dt, show that
dI/dt=-alphaI/omega (alpha= angular acceleration, omega=angular
velocity)
b) The quantity omega/omega(with a dot on it), where (omega with
a dot on it=domega/dt) is a natural time scale for the system's
change in angular frequency (to see this, think about the units).
Approximating...
On November 12, 2014, the Philae lander separated from the European Space Agency's Rosetta spacecraft, and made a lancing (after bouncing twice) on a comet known as 67P/Chunyumov -Gerasimenko. In this problem, we will explore the Gravitational environment that Rosetta (orbiting the comet) and Philae (on the comet's surface) experienced. On September 30, 2016, Rosetta crashed (as planned) on the comet. We will use a very simple model of the comet, modeling it as a perfect sphere. This is not...
Problem 2: Haley's Comet (A Real Life Example): Important: for this problem, complete all numerical work to a precision of at least six significant digits. Specifically: use the following precise values for astronomical constants: • Mass of the Sun = 1.98855 x 1030 kg • 1 AU = 149,597,870,700 meters . G=6.67384 x 10-11 N·m²/kg? Neptune Uranus Saturn Jupiter 05 2000 2005 2000----1995 2010 19921989 1988 1987 2024 1986 2061 2040 2060 2045 2050 2055 2056 2057 2058 2059 In...
8. A comet with unknown mass mc is in an elliptical orbit around the sun: R. Rp mc mc MS ū When the comet is at its parahelion R, it has a speed of up = 80km/s and at its aphelion R, it has a speed of va = 10km/s. For this problem suppose we do not know the mass of the sun M, or the value of Newton's constant G, but we can approximate the orbit of the earth...
Problem 3: The Rosetta spacecraft landed a probe on the comet Churyumov-Gerasimenko. It has a mass of appeoximately 1 x 10 kg and has an average density of approximately 400 kg/m. It is far from spherical, but for this problem go ahead and assume it is spherical. Estimate the radius, the acceleration due to gravity at the surface and the escape velocity from its surface. (10 points) Problem 4: A GPS satellite has a mass of 1940 kg and is...
6. When Halley's comet is closest to the Sun, it is at a distance of 8.823x1010 m from the Sun and at a speed of 5.46x 104 m/s. Given the comet's mass is about 2.2x1014 kg and the Sun's mass is 2.00x1020 kg: (a) Find the total mechanical energy of Halley's comet (8 points) (b) Assume all the time Hallye's comet is subject to the Sun's gravitational pull only. As the comet moves further away from the Sun, what will...
A comet orbits the Sun and loses mass at a constant rate of
30,000kg/s. The only force acting on the comet is the gravitational
force.
a) From the definition of torque in terms of angular momentum,
torque=dL/dt, show that
dI/dt=-alphaI/omega (alpha= angular acceleration, omega=angular
velocity)
b) The quantity omega/omega(with a dot on it), where (omega with
a dot on it=domega/dt) is a natural time scale for the system's
change in angular frequency (to see this, think about the units).
Approximating...
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H0:μ=56.9
H1:μ<56.9
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